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Unformatted text preview: Math 252 Exam 1 February 26, 2009 Musial Musial Name__—_—_
Instructions. Work each problem on the exam.. Where you are asked to solve an equation, make sure to ﬁnd all solutions. Show all work. 1. Solve the DE.
dy 1/2 =0.
d2: 1+:r2 2. Solve the DE.
3/ + 32621] = $2. 3. Solve the DE and give the largest intervals on which a solution can exist: my' + y 2 622:. 4. A tank initially contains 300 gallons of saline solution with salinity 5 lbs of salt per
gallon of solution. Solution having salinity 4 lbs of salt per gallon is pumped into the
tank at a rate of 8 gallons per minute, and solution leaves the tank at the same rate of
8 gallons per minute. Find the function A (t) which models the amount of salt in the
tank at any time, and ﬁnd the amount if salt in the tank after a long time. Be sure to draw a picture. 5. Show that the differential form (m2+y2)dm+(y+my)dy=0 is not exact. Multiply both sides by the integrating factor 1 + as and verify that the
resulting differential form is exact. Solve the DE. 6. For a series circuit containing only a resistor and an inductor, Kirchoff’s second law
states that the sum of the voltage drop across the inductor (L (cit/(125)) and the voltage
drop across the resistor (2R) is equal to the impressed voltage (E (t)) on the circuit.
Suppose that a 12volt battery is connected to an LR series circuit in which the induc~
tance is 0.2 henry and the resistance is 20 ohms. Determine the current 2' if the initial
current is 0.5 amp. 7. Solve the IVP
(w—y) dm+wdy=0,y(1) =1. 8. Solve the DE
_d_y + y = e—zy2
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 Spring '09
 Math

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